To provide an annual scholarship for 25 years, a donation of $50,000 is invested in an account for a scholarship that will start a year after the investment is made. If the money is invested at 5.5% per annum, compounded annually; determine the amount of each scholarship?

I would greatly appreciate it if I could be given some help.
Thanks so much in advance.

Jan 9th 2007, 05:41 AM

ticbol

Quote:

Originally Posted by asiankatt

To provide an annual scholarship for 25 years, a donation of $50,000 is invested in an account for a scholarship that will start a year after the investment is made. If the money is invested at 5.5% per annum, compounded annually; determine the amount of each scholarship?

I would greatly appreciate it if I could be given some help.
Thanks so much in advance.

I don't know if there is a ready formula for this. Let us derive one.

Let X = amount of scholarship to be deducted every year
A = amount of investment after any year
P = principal = $50,000 here.
r = rate of interest = 0.055 here.
n = number of years

In compounded annually,
A = P(1+r)^n

After year 1,
A = P(1+r)
Atfer withdrawal of X,
A = P(1+r) -X

After year 2,
A = [P(1+r) -X](1+r) = P(1+r)^2 -X(1+r)
After withdrawal of X,
A = P(1+r)^2 -X(1+r) -X

After year 3,
A = [P(1+r)^2 -X(1+r) -X](1+r)
A = P(1+r)^3 -X[(1+r)^2 +(1+r)]
After withdrawal of X,
A = P(1+r)^3 -X[(1+r)^2 +(1+r)] -X
.
.
After year 25,
A = P(1+r)^25 -X[(1+r)^24 +(1+r)^23 +(1+r)^22 +....+(1+r)]
After withdrawal of X,
A = P(1+r)^25 -X[(1+r)^24 +(1+r)^23 +(1+r)^22 +....+(1+r)] -X ------(i)
And that is now equal to zero.